Time dependent transformations in deformation quantization

We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time dependent coordinate transformations. This result considerably enlarges the set of possible phase space representations of quantum mechanics and makes it possible to construct a causal representation for the distributional sector of Wigner quantum mechanics.Comment: 16 pages, to appear in the J. Math. Phy

Half Quantization

A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical systems will be named half quantum. The aim of this paper is to derive the dynamical evolution of a general half quantum system from its full quantum formulation. The standard approach would be to use quantum mechanics to make predictions for the time evolution of the half quantum initial data. The main problem is how can quantum mechanics be applied to a dynamical system whose initial time configuration is not described by a set of fully quantum data. A solution to this problem is presented and used, as a guideline to obtain a general formulation of coupled classical-quantum dynamics. Finally, a quantization prescription mapping a given classical theory to the correspondent half quantum one is presented.Comment: 20 pages, LaTex file, Substantially revised versio

Coherent States Expectation Values as Semiclassical Trajectories

We study the time evolution of the expectation value of the anharmonic oscillator coordinate in a coherent state as a toy model for understanding the semiclassical solutions in quantum field theory. By using the deformation quantization techniques, we show that the coherent state expectation value can be expanded in powers of $\hbar$ such that the zeroth-order term is a classical solution while the first-order correction is given as a phase-space Laplacian acting on the classical solution. This is then compared to the effective action solution for the one-dimensional \f^4 perturbative quantum field theory. We find an agreement up to the order \l\hbar, where \l is the coupling constant, while at the order \l^2 \hbar there is a disagreement. Hence the coherent state expectation values define an alternative semiclassical dynamics to that of the effective action. The coherent state semiclassical trajectories are exactly computable and they can coincide with the effective action trajectories in the case of two-dimensional integrable field theories.Comment: 20 pages, no figure

Generalized Weyl-Wigner map and Vey quantum mechanics

The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantum mechanics, clarifying the relation between the two formulations is still missing. In this paper we present a covariant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantum mechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpretation of the Vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the Vey idiom. These features are illustrated through a simple example.Comment: 15 pages, LaTe

Subject age in P300 BCI

This paper presents a study about the amplitude, latency and distribution of P300 in twelve healthy volunteers (5 women and 7 men, aged between 19-70, with a mean of 35.5 years) that were submitted to two Novelty Oddball Paradigms. The difference between them is on stimulus modalities, which are visual and auditory. Usually, a P300-based brain computer interface has visual stimuli but we are also interested in making analogies between the two modalities. In both test modalities were presented 3 types of stimuli: a ‘standard’ stimulus, a ‘target’ stimulus, to which the subject must respond, and a ‘novel’ stimulus. Most of the subjects were students and are naive to the purposes of the experiment. The subject is not warned about the ‘novel’. We recorded scalp potentials from 18 channels distributed in a standard configuration 10-20 system. Target P300 had more relevance than novel P300 for a BCI application. Results show relevant differences in amplitude and latency in P300 signal for different ages. The Older subjects (>51 years) show smaller P300 amplitudes than younger. Therefore, the subject age must be taken into account when a P300 BCI application is implemented.Fundação para a Ciência e Tecnologia (FCT

An experience with Desmos in the study of the quadratic function

In this paper we present a didactic experience in the subject of Mathematics carried out in a distance learning context, on the topic Quadratic Function, using the digital and free platform Desmos. The use of this tool was determinant for the teaching and learning of quadratic function since its teaching took place in distance education, due to the pandemic situation. In a pandemic context, the use of tools to gauge student learning was a necessity, but practices such as the one described in this paper should be incorporated into a normal classroom environment, promoting discovery through graphical and algebraic manipulation.publishe

Efeito do cultivo de espécies vegetais sobre a população de Pratylenchus brachyurus na soja.

O presente trabalho, conduzido em casa de vegetação da Embrapa Soja, em Londrina, PR, no período de novembro/2011 a março/2012, teve como objetivos principais conhecer a reação de 23 espécies vegetais a Pratylenchus brachyurus e avaliar a influência da incorporação de suas fitomassas (parte aérea e raízes) no solo sobre as população do nematoide e performance da soja semeada, na sequência, nos vasos. Os fatores de reprodução (FR) de P. brachyurus obtidos nas diferentes espécies vegetais avaliadas variaram de zero (Crotalaria spectabilis, crambe, guandu ‘Fava Larga’ e tremoço branco) a 4,8 (Lab- Lab ‘Rongai’). As espécies vegetais com FR mais altos, independente da quantidade/composição da fitomassa incorporada, resultaram sempre em populações do nematoide mais elevadas nas raízes da soja (‘CD 202’). De todas as espécies vegetais testadas, apenas as C. specetabilis (FR=zero) e C. ochroleuca (FR=0,3) reduziram de fato a população original (1.000 nematoides) de P. brachyurus no vaso